Page 34 - Modern Spatiotemporal Geostatistics

Spatiotemporal Mapping in Natural Sciences 15

particularly with respect to four issues: scientific content, indetermination the-
sis, spatiotemporal geometry, and sources of physical knowledge.
Scientific content

In spatial statistics the mapping process is viewed mostly as an exercise of math-
ematical optimization involving data-fitting techniques (regression, polynomial
interpolation, spline functions, etc.). By ignoring the scientific content of the
mapping process, purely instrumental data-processing techniques can seriously
damage important scientific interpretations (e.g., they can lead to unrealistic
models of space/time correlation). If this is the case, one may soon be faced
with some kind of law of diminishing returns for geostatistics, inasmuch as
the problems of the rapidly developing new scientific disciplines are becoming
more complex and seemingly fewer new geostatistical methods with a sound
scientific rationale are available for their solution.
EXAMPLE 1.11: Mapping techniques based on spline functions seem attractive
to some, for they show a relative lack of conceptual bias (Thiebaux and Redder,
1987). These techniques have a conventional and purely instrumental character
(they merely include conditions on continuity, smoothness, and closeness to
data). Unfortunately, this lack of conceptual bias is usually accompanied by a
notable lack of scientific content. Indeed, no knowledge of the structural and
functional mechanisms of the natural process underlying the data is assumed.
Similarly, shortcomings of the kriging mapping techniques include:
(i.) the inability to account for important knowledge bases (see "Sources of
physical knowledge," p. 20), thus leading to maps which in many cases
do not reflect the opinion of the experts (see Bardossy et al., 1997);
(ii.) the lack of epistemic content (kriging's concern is merely how to deal
with data, rather than how to interpret and integrate them into the
understanding process);
(Hi.) the restrictive assumptions and approximations used, as well as the com-
putational problems (instability, high costs, etc.). See, e.g., Dietrich and
Newsam (1989) and Dowd (1992).
Is has been argued (e.g., Newton, 1997) that it is a characteristic of
immature scientific fields to rely primarily on taxonomy (collecting, describing,
and tabulating observational facts). This is particularly true for these fields
at their early stages of development, at which time classical geostatistics is,
indeed, a suitable tool. It usually takes a fierce struggle on the part of scientific
modelers to end the hegemony of taxonomists, and to allow such fields to
follow the theory-driven steps towards becoming a mature science. In the
context of such an effort, the methods of modern spatiotemporal geostatistics
are definitely more appropriate.

EXAMPLE 1.12: Biology is an example of a scientific field that was dominated
for decades by the culture of taxonomy. This culture was, perhaps, necessary
at the early stages of biology, but biology became a mature science only when